Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
const int maxn = 1e6 + 10;

int main() {
    int a, b, k;
    cin >> a >> b >> k;
    b--;
    if ((a == 0 && k > 0) || (k >= a + b && k > 0) || (b == 0 && k > 0)) {
        puts("No");
        return 0;
    }
    puts("Yes");
    string s, t;
    s = t = "1";
    if (a == 0 || b == 0 || k == 0) {
        for (int i = 0; i < a; i++) s += '0', t += '0';
        for (int i = 0; i < b; i++) s += '1', t += '1';
        cout << s << '\n' << t << '\n';
        return 0;
    }
    s += '1';
    t += '0';
    b--;
    a--;
    k--;
    for (int i = 0; i < k; i++) {
        char c;
        if (a > 0) c = '0', a--;
        else c = '1', b--;
        s += c;
        t += c;
    }
    t += '1';
    s += '0';
    while (b-- > 0) {
        s += '1';
        t += '1';
    }
    while (a-- > 0) {
        s += '0';
        t += '0';
    }
    assert(s.size() == t.size());
    assert(s >= t);
    
    cout << s << '\n' << t << '\n';
}